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Absolute Value Rules

Algebra rules for absolute values are listed below.

 

Piecewise Definition:
Square root definition:
Rules:

1.  |–a| = |a|

2.  |a| 0

3.  Products: |ab| = |a||b|

4.  Quotients: |a / b| = |a| / |b|

5.  Powers: |an| = |a|n

6.  Triangle Inequality:
         |a + b| |a| + |b|

7.  Alternate Triangle Inequality:
         |ab| |a| – |b|

CAREFUL!!     Sums:   

Differences:   

|a + b| is not the same as |a| + |b|

|ab| is not the same as |a| – |b|

 

See also

Absolute value of a complex number, triangle inequality (geometric)

 


  this page updated 28-jul-14
Mathwords: Terms and Formulas from Algebra I to Calculus
written, illustrated, and webmastered by Bruce Simmons
NCTM Web Bytes December 2004 Web Bytes March 2005 Web Bytes